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Scale-invariant uncertainty-averse preferences and source-dependent constant relative risk aversion


  • Costis Skiadas

    1. Kellogg School of Management, Northwestern University; c-skiadas@kellogg.northwestern.edu
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    • I thank Nabil Al-Najjar, Sandeep Baliga, Snehal Banerjee, Luciano De Castro, Eddie Dekel, Larry Epstein, Peter Klibanoff, Camelia Kuhnen, Bart Lipman, Dimitri Papanikolaou, Jacob Sagi, Todd Sarver, Tomasz Strzalecki, and two anonymous referees for helpful discussions and feedback. I am responsible for any errors.


Preferences are defined over payoffs that are contingent on a finite number of states representing a horse race (Knightian uncertainty) and a roulette wheel (objective risk). The class of scale-invariant (SI) ambiguity-averse preferences, in a broad sense, is uniquely characterized by a multiple-prior utility representation. Adding a weak certainty-independence axiom is shown to imply either unit coefficient of relative risk aversion (CRRA) toward roulette risk or SI maxmin expected utility. Removing the weak independence axiom but adding a separability assumption on preferences over pure horse-race bets leads to source-dependent constant-relative-risk-aversion expected utility with a higher CRRA assigned to horse-race uncertainty than to roulette risk. The multiple-prior representation in this case is shown to generalize entropic variational preferences. An appendix characterizes the functional forms associated with SI ambiguity-averse preferences in terms of suitable weak independence axioms in place of scale invariance.